1. Field of the Invention
The present invention relates to a method of and an apparatus for estimating characteristics of an unknown system using an adaptive filter in an echo canceller active noise control, equalizer, line enhancer, adaptive array, adaptive loudspeaker or a noise canceller.
2. Description of the Related Art
Transversal adaptive filters based on the learning identification method described in IEEE transactions on automatic control, Vol. AC-12, No. 3, pp. 282-287, 1967, USA (hereinafter referred to as Literature 1) are widely used in methods of and apparatus for estimating characteristics of an unknown system. The principles of operation of an acoustic echo canceller incorporating a transversal adaptive filter based on the learning identification method will be described below.
FIG. 1 of the accompanying drawings is a block diagram of an acoustic echo canceller based on the learning identification method. A system identification device is used as an echo canceller 100. A reference input signal 1 is converted by a loudspeaker 10 into an acoustic signal which is propagated through an acoustic path 11 as an unknown system and reaches, as an acoustic echo, a microphone 12. The microphone 12 converts the acoustic echo, with noise 2 added thereto, into an electric signal as an observed signal 3. An adaptive filter 101 effects a convolutional calculation on the reference input signal 1 and filter coefficients, and supplies the result as an output signal 5 to a subtractor 102. The subtractor 102 subtracts the output signal 5 from the observed signal 3, and produces a resultant error signal 4 as an output signal from the echo canceller 100, which is supplied to the adaptive filter 101. A power estimating circuit 103 estimates the power of the reference input signal 1, and supplies the estimated power to a divider 115. The divider 115 divides a positive constant .mu..sub.0 stored in a register 114 by the estimated power, and outputs the quotient as a step size 105. The adaptive filter 101 updates the filter coefficients in order to minimize the error signal 4, using the step size 105 supplied from the divider 115, the reference input signal 1, and the error signal 4.
The above process is expressed by equations as follows: It is assumed that the unknown system has an impulse response h.sub.i (i=0, . . . , N-1), the reference input signal 1 at a time "t" is represented by x(t), the noise 2 at the time "t" by n(t), and the observed signal 3 at the time "t" by d(t). The relationship between the reference input signal x(t), the noise n(t), and the observed signal d(t) is given by: ##EQU1## If the adaptive filter 101 has a tap number N and the filter coefficient is represented by w.sub.i (t) (i=0. . . , N-1), then the adaptive filter 101 produces an output signal y(t) expressed by: ##EQU2## From the equations (1) and (2), the error signal e(t) is indicated by: ##EQU3## Using the step size .mu.(t), the filter coefficient w.sub.i (t) is updated as follows: EQU w.sub.i (t+1)=w.sub.i (t)+.mu.(t)e(t)x(t-i) (4)
The step size .mu.(t) is given by: ##EQU4## where p.sub.x (t) is the power of the reference input signal 1 which is determined by the equation: ##EQU5## and .mu..sub.0 is a constant in the range of: EQU 0&lt;.mu..sub.0 &lt;2 (7)
The learning identification method updates the filter coefficient using the error signal e(t).
It can be seen from the equation (3) that the error signal e(t) contains the noise n(t) in addition to the system identification error h.sub.i -w.sub.i (t). When the noise n(t) is sufficiently smaller than the output signal of the unknown system, the filter coefficient can be updated properly and the characteristics of the unknown system can be identified according to the learning identification method. However, when the noise n(t) is larger, the filter coefficient cannot be corrected properly.
Furthermore, if the reference input signal x(t) is a non-stationary signal such as a speech signal, then the filter coefficient may not be updated properly even when the noise n(t) is relatively small. The reasons for this are considered to be as follows: Since the step size .mu.(t) is inversely proportional to the power P.sub.x (t) of the reference input signal x(t), the step size .mu.(t) is very large if the reference input signal x(t) is very small. The output signal from the unknown system 11 is very small, and the error signal e(t) contains larger noise n(t). Therefore, the filter coefficient w.sub.i (t) is updated greatly using the noise n(t) rather than the identification error h.sub.i -w.sub.i (t) with respect to the unknown system. As a result, the filter coefficients cannot be updated corrected properly.
As described above with reference to FIG. 1, the adaptive filter based on the learning identification method cannot update the filter coefficient properly when the noise is large.